Lecture 20: Arithmetic II Set Theory Politeness in Correspondence

Lecture 20:

Arithmetic II

Set Theory

Politeness in Correspondence

Arithmetic IIfunction [fankšən]:

example:f(x) the function of the variable x

derivative [di’rivətiv] – derivace an expression representing the rate of change of a function with respect to an independent variable

example:df(x,y) dx

-- the partial [‘pa:šəl] derivative of f(x,y) with respect to x

Arithmetic II

derive [di’raiv] – odvodit obtain a function or equation from another by a sequence of logical steps (e.g. by differentiation)

integral [intəgrəl] – integrál a function of which a given function is a derivative (which may express the area under the curve of a graph of the function)

example:

f (x)dx

-- the indefinite integral of f with respect to x

Arithmetic IIlogarithm [logəriδəm] – logaritmus

example:log x-- common logarithm of x

loga x-- logarithm (base a) of x

sine [sain], cosine [kəusain], tangent [tændžənt], cotangent [kəu’tændžənt]

sine – calculated as a ratio of the side opposite a given angle to the hypotenuse-- sine x, cosine x, tangent x, cotangent x

Arithmetic II

example:sin x, cos x, tg x, cotg x

|a| - the absolute value of aremainder [ri’meində] - zbytekquantity [kwontiti] – veličina

matrix [meitrix], pl. matrices [meitrisi:z] – matice a rectangular array of quantities or expressions in rows and columns that is treated as a single entity and manipulated according to particular rules

Σ – sum [sam] suma

Arithmetic II

The binomial [bai’nəumiəl] coefficient [kəui’fišənt] of the natural number n and the integer k is the number of combinations that exist.

The binomial coefficient of n and k is often read as "n choose k“.

Combinatorics [kəmbi:nə’to:riks]:

Arithmetic II

where n is the number of objects from which you can choose and k is the number to be chosen.

Set Theory

set – a collection of objects

union [ju:niən] of the sets A and B, denoted A, is the set whose members are members of at least one of A or B.

intersection [intə’sekšən] of the sets A and B, denoted A, is the set whose members are members of both A and B.

complement [komplimənt] of set A relative to set U, denoted AC , is the set of all members of U that are not members of A.

symmetric difference of sets A and B is the set whose members are members of exactly one of A and B. For instance, for the sets {1,2,3} and {2,3,4}, the symmetric difference set is {1,4}.

Set Theory

Cartesian [ka:’tiziən] product of A and B, denoted A B , is the set whose members are all possible ordered pairs (a,b) where a is a member of A and b is a member of B.

the power set of a set A - the set whose members are all possible subsets of A. For example, the powerset of {1, 2} is { {}, {1}, {2}, {1,2} }.

set A set Bintersection

Source: www.wikipedia.com

Politeness in Correspondence

Example of a poorly composed message:

Hi teacher,

I want the point for the question I wrote correctly.

Bye

Petr Balík Balíkovič

Politeness in Correspondence

Example of a correctly composed message:

Dear Sir/Madam,

I am sending this message with regard to your e-mail of April 2, 2007, where you say I might be awarded one more point for a question in my test I may have answered correctly. I wonder if you would be so kind as to check the test and make sure the question has been evaluated properly.

Thank you.

Yours faithfully

Daniel Kultivovaný

Politeness in Correspondence

Example of a correctly composed message:

Dear Mr. Dvořák,

do you think you could check my answer sheet and possibly award me one more point for the question you mentioned at today’s lecture? I am writing this e-mail since I am not completely sure of what alternatives I have selected for the question.

Thank you.

Yours sincerely (Best regards, Kind regards, Regards, All the best, Best wishes, …)

Petra Poloformální

Politeness in Correspondence

The principal rules to remember:

i. Always reply to any e-mail you receive letting the sender know you have received it and you have not ignored its contents. You should do so even if it were in the form of a simple ‘Allright’ note.

ii. Beware of the person who does not reply to your e-mail despite receiving it since there is always a problem to surface in the future!! That is, such a person is likely to turn out slapdash, boorish, conceited, complacent, or having any other negative trait that might eventually get you in trouble!!

Homework

Specialist Reading:

• Computing Support

• Raiding Hard Drives

End of Lecture Series